Balanced Bipolar Intuitionistic Fuzzy Graphs

In this paper, we discuss balanced bipolar intuitionistic fuzzy graphs and study some of their properties 1.Introduction Graph theory is developed when Euler gave the solution to the famous Konigsberg bridge problem in 1736. Graph theory is very useful as a branch of combinatorics in the field of geometry, algebra, number theory, topology, operations research, optimization and computer science. Rosenfeld[2] developed the structure of fuzzy graphs, obtaining analogs of several graph theoretical concepts. Later on, Bhattacharya[3] gave some remarks on fuzzy graphs, and some operations on fuzzy graphs were introduced by Mordeson and Peng[4]. The complement of a fuzzy graph was defined by Mordeson and Nair[5] and further studied by Sunitha and Vijayakumar [6]. Akram[7] has introduced Bipolar fuzzy graphs and investigated their properties. Balanced graph first arose in the study of random graphs and balanced IFG defined here is based on density functions. A graph with maximum density is complete and graph with minimum density is a null graph. There are several papers written on balanced extension of graph [8] which has tremendous applications in artificial intelligence, signal processing, robotics, computer networks and decision making AlHawary [9] introduced the concept of balanced fuzzy graphs and studied some operations of fuzzy graphs. Shannon and Atanassov[10] introduced the concept of intuitionistic fuzzy relations and intuitionistic fuzzy graphs, and investigated some of their properties. Parvathi et al[11].defined operations on intuitionistic fuzzy graphs.Karunambigai et al [2] introduced balanced intuitionistic fuzzy graphs and studied some of their properties.In 2015, D.Ezhilmaran and K.Sankar[16] have introduced bipolar intuitionistic fuzzy graphs. In this paper, we discussed balanced bipolar intuitionistic fuzzy graphs and study some of their properties.